Open Access

Asymptotic Expansions for Higher-Order Scalar Difference Equations

Advances in Difference Equations20072007:067492

DOI: 10.1155/2007/67492

Received: 26 November 2006

Accepted: 23 February 2007

Published: 11 April 2007


We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation. As a consequence, we obtain an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity. The proof is based on the inversion formula for the z -transform and the residue theorem.


Authors’ Affiliations

Department of Mathematical Sciences, Florida Institute of Technology
Department of Mathematics and Computing, University of Veszprém


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© R. P. Agarwal and M. Pituk. 2007

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